Problem: $K$ is the midpoint of $\overline{JL}$ $J$ $K$ $L$ If: $ JK = 7x - 9$ and $ KL = 8x - 13$ Find $JL$.
A midpoint divides a segment into two segments with equal lengths. ${JK} = {KL}$ Substitute in the expressions that were given for each length: $ {7x - 9} = {8x - 13}$ Solve for $x$ $ -x = -4$ $ x = 4$ Substitute $4$ for $x$ in the expressions that were given for $JK$ and $KL$ $ JK = 7({4}) - 9$ $ KL = 8({4}) - 13$ $ JK = 28 - 9$ $ KL = 32 - 13$ $ JK = 19$ $ KL = 19$ To find the length $JL$ , add the lengths ${JK}$ and ${KL}$ $ JL = {JK} + {KL}$ $ JL = {19} + {19}$ $ JL = 38$